This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Surface Area of a Right Circular Cone”.

1. In the figure given below, the cone is right circular cone.

a) True

b) False

View Answer

Explanation: For the cone to be right circular cone, the line joining its vertex to the centre of its base have to be perpendicular to the base. (As shown in the below figure)

But we can see in the given figure that the line is not perpendicular to the base, hence the given cone is not right circular cone.

2. The total surface area of a cone of base radius “r” and slanted height “l” is equal to __________

a) πrl + 2πr^{2}

b) 2πrl + 2πr^{2}

c) πrl + πr^{2}

d) 2πr^{2}

View Answer

Explanation: Total surface area of a cone of base radius “r” and slanted height “l”

= Curved surface area of a cone + Base area of a cone

= πrl + πr

^{2}.

3. What is the total surface area of a cone of radius 7cm and height 24cm? (Take π = \(\frac{22}{7}\))

a) 710 cm^{2}

b) 704 cm^{2}

c) 700 cm^{2}

d) 725 cm^{2}

View Answer

Explanation: Given, r = 7cm and h = 24cm

From the figure,

We can say that according to the Pythagoras theorem, l

^{2}= r

^{2}+ h

^{2}

= 7

^{2}+ 24

^{2}

= 625

Therefore, l = 25cm

We know that total surface area of a cone = πrl + πr

^{2}

= πr (l + r)

= \(\frac{22}{7}\) * 7 (25+7)

= 704 cm

^{2}.

4. The curved surface area of a cone is 1980 cm^{2} and its radius is 21cm, what is the slanted height of a cone? (Take π = \(\frac{22}{7}\))

a) 25cm

b) 28cm

c) 35cm

d) 30cm

View Answer

Explanation: We know that the curved surface area of a cone = πrl

πrl = 1980

\(\frac{22}{7}\) * 21 * l = 1980

l = 30cm.

5. A tent of conical shape of base radius 28m and slanted height 20m is to be made from a certain material. What is the total cost of clothing material if the rate of material is ₹80/m^{2}? (Take π = \(\frac{22}{7}\))

a) ₹140800

b) ₹150000

c) ₹130500

d) ₹140000

View Answer

Explanation: The curved surface are of a conical tent = πrl

= \(\frac{22}{7}\) * 28 * 20

= 1760m

^{2}

Cost of 1m

^{2}of material = ₹80

Hence, the total cost of 1760m

^{2}= 1760 * 80

= ₹140800.

6. A vessel of conical shape of radius 14cm and slanted height 20cm is to be coloured. What is the cost of painting at a rate of ₹2/cm^{2}? (Take π = \(\frac{22}{7}\))

a) ₹1540

b) ₹1660

c) ₹1760

d) ₹1500

View Answer

Explanation: We know that curved surface area of We know that the curved surface area of a cone = πrl

For the given conical vessel, r = 14cm and l = 20cm (given)

Hence, curved surface area of vessel = πrl

= \(\frac{22}{7}\) * 14 * 20

= 880cm

^{2}

Now, the cost of painting 1cm

^{2}area = ₹2

Then the cost of painting 880cm

^{2}area = 880*2

= ₹1760.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 9**.

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